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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Limits of integral series

Suppose we have the series of functions: \begin{equation} F(x)=\sum_{n=1}^{\infty} f_n(x) \end{equation} where convergence is uniform. Additionally, consider the partial functions of the series: \begi …
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